Related papers: Generalising Aumann's Agreement Theorem

One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…

Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalisation is possible by reducing the number of quantum postulates used by Busch.…

The premise of the Multi-disciplinary Conference on Reinforcement Learning and Decision Making is that multiple disciplines share an interest in goal-directed decision making over time. The idea of this paper is to sharpen and deepen this…

Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive…

Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system.…

We study games of chance (e.g., pokers, dices, horse races) in the form of agents' first-order posterior beliefs about game outcomes. We ask for any profile of agents' posterior beliefs, is there a game that can generate these beliefs? We…

We propose a number of powerful dynamic-epistemic logics for multi-agent information sharing and acts of publicly or privately accessing other agents' information databases. The static base of our logics is obtained by adding to standard…

This paper addresses the adaptive consensus problem in uncertain multi-agent systems, particularly under challenges posed by quantized communication. We consider agents with general linear dynamics subject to nonlinear uncertainties and…

We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of…

We introduce a new way of quantifying the degrees of incompatibility of two ob- servables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all…

We study a problem where a group of agents has to decide how a joint reward should be shared among them. We focus on settings where the share that each agent receives depends on the subjective opinions of its peers concerning that agent's…

Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the…

Recently, a delicately designed Gedankenexperiment was proposed to check the self-consistence of quantum theory in the description of the agents who are using this theory. It was demonstrated that the quantum theory is inconsistent. Here a…

Bell's 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbach's Principle of Common Cause. Despite being a hallmark of scientific thought, dropping the principle has been…

This work studies the learning process over social networks under partial and random information sharing. In traditional social learning models, agents exchange full belief information with each other while trying to infer the true state of…

This work studies the distributed learning process on a network of agents. Agents make partial observation about an unknown hypothesis and iteratively share their beliefs over a set of possible hypotheses with their neighbors to learn the…

This paper introduces the notion of `commonly knowing whether', a non-standard version of standard common knowledge which is defined on the basis of `knowing whether', instead of standard `knowing that'. After giving five possible…

Theory of Mind (ToM) -- the ability to understand that others can have differing knowledge and goals -- enables agents to reason about others' beliefs while planning their own actions. We present a novel approach to multi-agent cooperation…

We consider the relation between knowledge and certainty, where a fact is known if it is true at all worlds an agent considers possible and is certain if it holds with probability 1. We identify certainty with probabilistic belief. We show…

In the classical Approximate Majority problem with two opinions there are agents with Opinion 1 and with Opinion 2. The goal is to reach consensus and to agree on the majority opinion if the bias is sufficiently large. It is well known that…